Holmium(III)–Carbon Nanodots Hybrid for Fluorescent Quenching Effect in the Oxalate Detection (C₂O₄)^2– and Their Different Photoinduced Charge Transfer Processes

Abstract

In this work, carbon nanodots (CNDs) were synthesized via a pyrolysis carbonization method using Rosa damascena petals. The synthesized CNDs exhibit optical absorption in the UV region, with a tail extending out into the visible range. When these CNDs interact with Ho³⁺ ions through charge transfer processes, they form an REⁿ⁺-CNDs hybrid (Rare Earth-CNDs hybrid), resulting in fluorescence quenching in an aqueous solution. This fluorescence can be recovered by allowing the Ho³⁺-CNDs hybrid to interact with the oxalate anions. An in silico study supports this mechanism through density functional theory (DFT) analysis, which involves a charge transfer process in discrete systems of functionalized Ho³⁺-C₆₀. The above plot provides an approximation of the behavior of CNDs and highlights the electrostatic interaction in the [Ho­(C₂O₄)₃]^3– complex. Based on this phenomenon, an environmentally friendly fluorescent turn-off/on sensor was developed to detect holmium ions Ho³⁺ and oxalate ions in an aqueous solution. The quantitative detection of Ho³⁺ ranges from 1.0 × 10^–5 to 1.0 × 10^–4 M, while oxalate concentrations vary from 4.5 × 10^–5 to 3.6 × 10^–4 M. The concentration of both species exhibited a linear relationship with the fluorescence intensity, characterized by a correlation coefficient of R ² = 0.9801 and a Stern–Volmer constant K _SV = (1.09 × 10⁴ ± 6 × 10²) M^–1. In addition, the Laplacian and electronic values obtained, within Bader's quantum theory of atoms in molecules, revealed ionic interactions between holmium­(III) and oxalate anions. Moreover, an analysis of the Mulliken and Hirshfeld charges confirmed a charge transfer process from CNDs to Ho³⁺.

1. Introduction

Carbon dots (CDs) have garnered increasing interest due to their photoluminescent applications, such as developing analyte sensors. , These nanomaterials are primarily classified into four types: carbon nanodots (CNDs), carbon quantum dots (CQDs), graphene quantum dots (GQDs), and polymer dots (PDs). Each of these types is distinguished by its internal structure, which can be amorphous, quasi-spherical, or crystalline, as well as by the nature of its photoluminescence (PL) and size range. In particular, CNDs lack a crystalline lattice, and their PL originates from the presence of fluorophore molecules or emitting functional groups on the surface of the nanoparticles. Furthermore, PL can occur through a coupling mechanism between the core and surface of the carbon particle at the electronic level. This PL is attenuated when the functional groups on the CNDs interact with species such as nanoparticles, heavy metal ions, or other analytes of interest, − or via an internal photoswitching mechanism.

One of the key features of CNDs is their high water solubility, biocompatibility, and low toxicity. In addition, CNDs are involved in charge-transfer processes, acting as either electron donors or acceptors. These properties open up a range of applications in biotechnology fields, including bioimaging, drug delivery, medical diagnostics, and biosensors. For example, alginate microspheres loaded with Ho³⁺ complexes can be used as imaging agents, and if radioactive, they can be employed for local radiotherapy of tumors. In addition, the most stable and common lanthanide complexes are those with oxygen ligands, which typically present coordination numbers of 8 or 9. However, exceptions exist, such as the La­(III) complex, which features six equidistant La–N interactions, where N denotes an amide ligand.

In the current study, a fluorescence turn-off/on method is presented for detecting holmium­(III) ions and oxalate anions, based on the formation of Ho³⁺-CNDs hybrids and the [Ho­(C₂O₄)₃]^3– complex. These hybrids are formed through the interaction between Ho³⁺ ions and the peripheral functional groups on the CNDs surface. This process occurs through a photoinduced charge transfer mechanism, as evidenced by an in silico study implementing density functional theory (DFT). All synthesized CNDs exhibit a certain number of oxygen atoms on their surface, featuring functional groups such as carbonyls (carboxylates, ketones, aldehydes, etc.) and hydroxyl groups. All of them can interact with Ho³⁺ ions, via photoinduced charge transfer processes, leading to a fluorescence quenching effect. The determination of oxalate, a bidentate ligand, is based on the formation of a complex between Ho³⁺ and the oxalate ions with a predominantly electrostatic interaction. This process, which is stronger than charge transfer, displaces Ho³⁺ from the surface of the CNDs, thereby recovering the fluorescence intensity of the CNDs. This aligns with recent advances in heavy metal sensors using carbon-based materials and Schiff bases, some of which also apply DFT. Unlike those studies, this work focuses on the less-explored lanthanide ion Ho³⁺ and its combined detection with oxalate, offering a distinct approach. , In the current study, the CNDs were synthesized using a bottom-up approach derived from the calcination of Rosa damascena petals at various temperatures via a pyrolysis process. , This methodology enables the production of CNDs with photoluminescent properties, offering an innovative approach that contributes to the sustainability of nanomaterial production.

2. Experimental and Computational Methods

2.1. Experimental Details

The rose petals used in the experiment were purchased from a local market. These petals were not washed and were directly analyzed by infrared spectroscopy to eliminate the possibility of pesticide residues. Four samples, each containing 6.0 g of petals, were subjected to calcination at 300 °C for different durations (1, 2, 3, and 4 h) in a Type FD1500 M muffle furnace. After calcination, the samples were pulverized to form fine powders. The four samples were subsequently characterized by infrared spectroscopy. The Fourier transform infrared (FTIR) spectra were recorded using a PerkinElmer FTIR system, model Spectrum GX, with Spectrum software. The data were collected using an ATR accessory in the range of 3500–500 cm^–1, with a resolution of 4.0 cm^–1 and a step size of 1.0 cm^–1. The sample calcined at 300 °C for 2 h was chosen as the precursor for the CNDs. To prepare the CNDs, 0.2 g of the selected sample was dissolved in 500 mL of deionized water and subjected to centrifugation at 4000 rpm for 30 min. The solution was then filtered through filter paper with a pore size of 110 μm. Finally, a pale-yellow solution containing the CNDs was collected.

To determine the interaction and impact of Ho³⁺ on the CNDs, the concentration of the CNDs was kept constant across all calibration points, and all Ho³⁺ solutions were prepared using deionized water to minimize interference from spectator ions. A 0.01 M stock solution of Ho­(NO₃)₃·5H₂O, a reagent purchased from Aldrich Chem. Co., was used for the preparation of the solutions. Ten milliliters of CNDs were prepared by adding the Ho³⁺ solution, with concentrations ranging from 0.0 to 9.0 × 10^–5 M. The solutions were characterized by UV–vis spectroscopy using a PerkinElmer spectrometer, and the PL spectra were recorded using a PerkinElmer spectrophotometer.

To analyze the impact of oxalate presence on the Ho³⁺-CNDs system, calibration samples were prepared by adding 10 μL of a Ho³⁺ working solution at a concentration of 9.0 × 10^–5 M, which was then diluted to 10 mL with the CNDs solution. Successive aliquots of an oxalate solution, with concentrations ranging from 0.0 to 3.6 × 10^–4 M, each of 10 μL, were then added to the Ho³⁺-CNDs solution. These samples were characterized by using UV–vis spectroscopy and fluorescence spectrophotometry.

2.2. Computational Details

In order to elucidate the charge transfer processes involving Ho³⁺ ions, CNDs, and the [Ho­(C₂O₄)₃]^3–complex, a DFT study was performed. The B3LYP functional was selected due to its proven reliability in modeling organic molecules. The basis set for carbon, oxygen, and hydrogen atoms was 6–31G, while the def2-TZVP basis set was applied for Ho³⁺. Thus, the complete computational method employed was B3LYP/def2-TZVP for Ho³⁺ and B3LYP/6–31G for all other atoms. These calculations were carried out using Gaussian 16 C.01. For comparison purposes, a larger basis set, including polarization and diffusion functions, was discussed at the end of the Section . To ensure the reliability of the selected correlation-exchange functional for accurately describing the electronic structure of the rare-earth-metal- and holmium-based systems, a validation step was first carried out by computing three ionization energies of the isolated Ho atom using various methods. This enabled a direct comparison with experimental data and provided a means to evaluate both the accuracy and convergence behavior of each tested functional. The PBE and PBE0 functionals were tested but failed to converge for both the Ho³⁺-CNDs hybrids and the [Ho­(C₂O₄)₃]^3– complex. In contrast, B3LYP converged successfully in both cases. Furthermore, the third computed vertical ionization energy (I ₃ = 22.631 eV) obtained with B3LYP closely matches the experimental value of 22.790 eV, highlighting its reliability for this system. To assess the accuracy of the tested methods, we evaluated the mean squared error (MSE, (eq )), mean absolute percentage error (MAPE, (eq )), mean absolute error (MAE, (eq )), and root mean squared error (RMSE, (eq )), as summarized in Table . The computation of the metrics was performed as described in the following equations:

$$\mathrm{MSE}=(1/n)\sum (y_{\mathrm{i}}-{\widehat{y}}_{\mathrm{i}}{)}^2$$ 1

$$\mathrm{MAPE}=(1/n)\sum |(y_{\mathrm{i}}-{\widehat{y}}_{\mathrm{i}})/y_{\mathrm{i}}|\times 100\%$$ 2

$$\mathrm{MAE}=(1/n)\sum |y_{\mathrm{i}}-{\widehat{y}}_{\mathrm{i}}|$$ 3

$$\mathrm{RMSE}=\stackrel{1/2}{\left((1/n)\sum (y_{\mathrm{i}}-{\widehat{y}}_{\mathrm{i}}{)}^2\right)}$$ 4

where ŷ _i represents the predicted value, n is the number of observations, and y _i corresponds to the observed value. In this study, ŷ _i refers to the calculated ionization energy by DFT, while y _i denotes the experimental ionization energy.

1. Ionization Energies of Holmium Computed Using Different Functionals, with the Corresponding Error Metrics and Comparison to Experimental Values .

method used	I 1 (eV)	I 2 (eV)	I 3 (eV)	I 4 (eV)	MAPE [%]	MSE [eV2]	RMSE [eV]	MAE [eV]
PBE	5.998	12.710	23.814	44.277	4.226	1.250	1.118	0.933
PBE0	6.878	11.706	22.438	43.327	4.578	0.379	0.615	0.523
B3LYP	7.130	11.954	22.631	43.600	5.778	0.613	0.783	0.630
experimental	6.022	11.781	22.790	42.520

^aExperimental references were annotated accordingly.

Resembling the spherical-like geometry of the CNDs, modified fullerenes C₆₀ were proposed as models to perform computational calculations and provide an initial approximation of the interactions between Ho³⁺ and CNDs. Thus, a single-ion approach was employed to model the interaction between the modified fullerenes and the Ho³⁺ ions. These modifications to the fullerene were based on the functional groups identified in FTIR analysis, as detailed in the subsequent section. To save computational resources, only three functional groups were included: primary alcohol, carboxylate, and anhydride groups, as these contain oxygen atoms capable of interacting with Ho³⁺, as predicted by Pearson’s hard–soft acid–base (HSAB) theory. The system C₆₀-CO-Ho³⁺will be referred to as a primary alcohol in the following sections. Functional groups such as acetylene and methylene were excluded because of the lack of reactive oxygen atoms. In the case of [Ho­(C₂O₄)₃]^3–, although Ho³⁺ commonly adopts coordination number of 8 or 9, as is typical for lanthanide ions, coordination numbers as low as 6 have been reported in the case of La­(III). For the computational model, the configuration with three oxalate anions yielded the minimum energy and was therefore selected as the most stable structure for this study, acknowledging that alternative coordination numbers could exist.

The ground state structures of the hybrid fullerene-functional group systems were obtained from various configurations proposed. Initial calculations placed the Ho³⁺ ion at several positions, maintaining a separation of 2 Å from the modified fullerene. All of the modified species were considered in their respective ground state geometries, determined using zero-point vibrational energy corrections. Only configurations with all real vibrational frequencies were retained for further analysis. The same process was considered for the [Ho­(C₂O₄)₃]^3– complex and the isolated Ho³⁺.

The Bader’s Quantum Theory of Atoms in Molecules (QTAIM) was employed to provide a quantum mechanical picture of the structure and interactions of the complexes obtained. This method enables the characterization of the chemical bond type between Ho³⁺ ions and both CNDs and [Ho­(C₂O₄)₃]^3–. The topology analysis of the electron density was conducted using the Multiwfn 3.8 software package, , to obtain the bonding critical points (BCPs) and Bader’s molecular graph. Additionally, to investigate the charge transfer process, Mulliken and Hirshfeld charge analyses were carried out on the complexes both with and without Ho³⁺, employing the Multiwfn software for these calculations.

3. Results and Discussion

The evidence for the presence of functional groups on the surface was obtained from the structural characterization of CNDs samples using FTIR at different calcination times (Figure ). The FTIR spectrum of the calcined CNDs sample at a time of 1 h revealed several key features. A stretching vibrational mode of the C–O, from a primary alcohol at 1017 cm^–1 (ν–CO). Two bands corresponding to a carboxylate anion were identified: a strong asymmetrical stretching band at 1600 cm^–1 (ν_asy–COO^–1) and a weaker symmetrical stretching band at 1400 cm^–1 (ν_sym–COO^–1). Additionally, a strong band at 1047 cm^–1 was attributed to the stretching vibration of unconjugated straight-chain anhydrides C–CO–O–CO–C. Near 750 cm^–1, a band corresponding to the methylene rocking vibration (ρ–CH₂) appears. Finally, a band at 2300 cm^–1 was associated with disubstituted acetylenes, where the substituents are different (ν-CC).

1.

Infrared spectrograms of the CNDs calcined at different times at T = 300 °C.

The spectrograms indicate that as the pyrolysis time increases during the formation of CNDs, the signals at 1600 and 1400 cm^–1 intensify. At the time, the signal at 1017 cm^–1, attributed to a (ν-CO) vibration of a primary alcohol, diminishes. This change highlights that the preparation process of the CNDs was carried out in a noninert atmosphere, promoting oxidation reactions that result in the predominance of carboxylate groups. The identified functional groups are derived from organic acids, flavonoids, and tocopherols present in the rose petals (R. damascena). −

3.1. Structural Characterization of the CNDs

The morphology, size distribution, and structural order of CNDs were evaluated by using transmission electron microscopy (TEM), selected area electron diffraction (SAED), and X-ray diffraction (XRD). TEM and SAED analyses were performed using a JEOL ARM-200F scanning transmission electron microscope (STEM) operated at 200 kV, located at the Central Electron Microscopy Laboratory of UAM-Iztapalapa (Figure A). Low-magnification TEM micrograph, where the nanoparticles appear well dispersed with no significant aggregation. The particle size histogram (Figure B), obtained from statistical analysis of multiple particles, shows an average diameter of 13.7 ± 4.7 nm, indicating a moderately narrow distribution. In the TEM image (Figure C), the CNDs display a uniform granular texture with no observable lattice fringes, suggesting an amorphous structure. This is further supported by the SAED pattern (Figure D), which exhibits a diffuse halo rather than defined diffraction rings, typical of amorphous or turbostratic carbon structures.

2.

(A) TEM micrograph of monodispersed CNDs. (B) Size distribution histogram (13.7 ± 4.7 nm). (C) TEM image showing the amorphous structure. (D) SAED pattern with diffuse halo, a characteristic of amorphous carbon.

The XRD pattern (Figure ) displays a broad peak centered at 26.37° (2θ), typically associated with the (002) reflection of disordered carbon. While this feature is common to both amorphous and turbostratic carbon, the latter is distinguished by its graphene-like layers with rotational or translational disorder rather than a complete lack of structure. In this work, the CNDs exhibit a predominantly amorphous character with no clear evidence of turbostratic stacking, as supported by the absence of lattice fringes in TEM images and the diffuse nature of the SAED pattern. The annealed powders were structurally characterized by XRD using a Bruker D8 Advance diffractometer with Cu Kα radiation. Data were collected over a 2θ range from 2 to 70°, with a step size of 0.020415° and a counting time of 20.0 s per point. The diffraction data were analyzed using PROFEX 5.3 software.

3.

X-ray diffraction pattern of the CNDs showing a broad peak around 26.37° (2θ), corresponding to the (002) plane of disordered carbon, a characteristic of an amorphous structure.

3.2. UV–Vis Spectroscopic Analysis of Ho³⁺-CNDs Hybrids and [Ho­(C₂O₄)₃]^3–Complex

The synthesized CNDs were characterized using ultraviolet–visible (UV–vis) spectroscopy, which revealed strong blue fluorescence under 365 nm excitation through UV lamp irradiation. The CNDs exhibit a prominent absorption band at 250 nm, with a weaker absorption band at 280 nm and a tail extending into the visible range. Absorption at 250 nm is attributed to the π–π* transition of aromatic C–C bonds, while absorption at 280 nm is attributed to the n−π* transition associated with functional groups on the surface of the CNDs (Figure ). Similar to the structural changes observed with varying pyrolysis times, as reflected in the FTIR study, the four UV–vis spectra show a marked decrease in the absorption intensity. This decrease is again attributed to the removal of functional groups, such as carbonyl (CO), which are replaced by carboxylate groups in the condensed phase and CO₂ in the gaseous phase. It is also important to note that a photoblinking process occurs in CNDs, governed by a Dexter-type electron transfer mechanism from fluorescent functional groups (donors, D) to charge-accepting sites on the surface (A_n).

4.

UV–vis spectrograms of the CNDs calcined at different times at T = 300 °C showing two bands associated with electronic transitions π–π* and n−π*.

The UV–vis absorption spectrum of the CNDs showed a linear decrease in absorbance as the concentration of Ho³⁺ increased from 0 to 60 μM (Figure ). This behavior is attributed to the charge transfer between the functional groups on the surface of the CNDs, as well as between the sp³/sp² carbon domains and the Ho³⁺ ions. Given the highly electropositive nature of lanthanides, a photoinduced electron transfer process occurs, leading to the formation of the Ho³⁺-CNDs hybrid and initiating fluorescence quenching based on the reduced interaction of free CNDs with UV–vis radiation. This is reflected in the observed decrease in absorbance intensity.

5.

Absorption spectra of Ho³⁺-CNDs hybrids in aqueous solutions with varying concentrations of holmium­(III); [Ho³⁺] = 1.4 × 10^–5 to 6.0 × 10^–5 M.

Upon addition of oxalate anions in concentrations ranging from 96 to 900 μM to a constant concentration Ho³⁺-CNDs hybrid system, the absorbance of the CNDs increased consistently (Figure ). This increase can be explained by the formation of a complex between Ho³⁺ and oxalate ions, a bidentate ligand, which forms stable complexes due to its π-acidic nature and its binding site being one of the hardest bases according to Pearson’s HSAB theory. This leads to the release of lanthanide ions from the surface of the CNDs, favoring electrostatic interactions over photoinduced charge transfer. As a result, the charge transfer process is reduced, allowing the CNDs to recover part of their absorption capacity and, consequently, their characteristic fluorescence. To calculate the bandgap energy (E _g) for the CNDs and Ho³⁺-CNDs hybrid, we analyzed the absorption spectra, ranging from 200 to 600 nm. The above, considering the energy of the incident photon (E _f) and the absorption coefficient, α, using the model proposed by Tauc and Meth. − To estimate the bandgap energy, we plotted (αhν)² versus energy (eV) for the Ho³⁺-CNDs hybrids, assuming a direct transition, and performed a linear fit. The bandgap energy was determined from the intercept with the energy axis, and it was found to vary with respect to the concentration of Ho³⁺, as shown in Table . It can be observed that the bandgap increases as the Ho³⁺ concentration rises from 0 to 60 μM (Figure ).

6.

Absorption spectra of Ho³⁺-CNDs hybrid with a holmium­(III) concentration of [Ho³⁺] = 60 μM, mixed with different concentrations of oxalate, [C₂O₄]^2– = 9.6 × 10^–5 to 3 × 10^–4 M.

2. Bandgap Energy (eV) and Urbach Energy (eV) for Different Ho³⁺-CNDs Hybrids Systems.

Ho3+-CNDs hybrids (μM)	E g (eV)	E u (eV)
a-0	4.70	1.72
b-14	4.91	1.12
c-28	5.07	0.89
d-42	5.12	0.77
e-56	5.15	0.70
f-60	5.16	0.69

7.

Bandgap energy estimate by plot of (αhν)² for Ho³⁺-CNDs hybrids systems against the energy of the incident photon (eV) (a–f) for different concentrations of holmium­(III).

Tepliakov et al. proposed a quantum chemical approach in which the degree of hybridization is related to the HOMO–LUMO bandgap, where HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) represent the frontier orbitals involved in electronic transitions. Based on the high E _g value of our CNDs, it is assumed that the sp² hybridization percentage is very low, with sp³ carbon domains predominating in the system. As a result, the hybridization factor, denoted as η, takes values that diverge in the aforementioned model. This divergence arises from the interaction of hydrogen atoms at the periphery, likely due to hydrogen-bonding interactions with the surrounding aqueous environment. The electrons in the sp³ domains exhibit strong interaction with the aqueous medium, leading to a significantly larger energy gap along with the fact that a high percentage of sp³ hybridizations implies an increase in the material’s density, which shows a linear dependence with the opening of the bandgap. The determination of this gap also supported the quasi-spherical geometry of the CNDs, as it correlates with the sp³/sp² ratio and the degree of disorder in the system. Moreover, the study shows that the percentage of sp² domains does not primarily contribute to the optical response of the CNDs. Instead, the PL effect is mainly determined by the nature of the functional groups present, which are related to the bandgap value of the system, as shown by Choi et al. when modifying CNDs structures with electron-accepting atoms that reduce the E _g values.

The width of the Urbach tail was obtained by plotting ln α against E _f (Figure ). For the six Ho³⁺-CNDs hybrids with different concentrations of Ho³⁺, a linear fit was established in the linear portions of the curves, for which the inverse of their slope was calculated, and this value is the Urbach energy. The value of the Urbach energy indicates the effect of strong disorder on the electronic states, so when the concentration of Ho³⁺ increases, the Urbach energy decreases linearly. When impurities, such as Ho³⁺ ions, are introduced into the CNDs, localized disorder sites are created within the material’s structure, which affects the distribution of electronic states in the energy gap. Metallic ions or defects introduce additional levels in the material’s electronic structure, increasing the density of states in the gap. This, in turn, influences the shape of the Urbach tail. As the concentration of Ho³⁺ increases, more disorder sites and defects are introduced into the CNDs’ structure, which could initially increase the density of states in the gap and broaden the Urbach tail, thereby increasing the Urbach energy. However, in this case, it is observed that as the concentration of Ho³⁺ increases, the Urbach energy decreases. This behavior may be related to the fact that Ho³⁺ ions induce a reorganization of the electronic states in the CNDs, possibly creating greater homogeneity or structural stability rather than introducing additional disorder. Moreover, lanthanide ions, such as Ho³⁺, have high electropositivity, and their 4f electrons can interact strongly with the electronic states of the CNDs. The above especially in terms of charge transfer or electrostatic interactions. These types of interactions could modify the distribution of the material’s energy levels, reducing the dispersion of the electronic states and, consequently, the degree of disorder in the system. At higher concentrations of Ho³⁺, stronger interactions between the ions could occur, leading to structural reorganization that reduces disorder at both the macroscopic and the bandgap levels. As a result, the decrease in Urbach energy reflects a reduction in the material’s disorder and an increase in the structural stability of the CNDs.

8.

Width of the Urbach tail (a–f) for different concentrations of holmium­(III) was obtained by plotting ln (α) against the photon energy.

3.2.1. Fluorescent Quenching in Ho³⁺-CNDs/[Ho­(C₂O₄)₃]^3– Systems

The behavior of the fluorescence of the CNDs synthesized against the different concentrations of Ho³⁺ from 0 to 90 μM (a–j) is shown in the photoluminescence spectra (Figure ). It is observed that at a higher concentration of holmium­(III), the fluorescence intensity of the CNDs is extinguished. The charge transfer interaction between Ho³⁺ and the functional groups on the surface of the CNDs affects the electronic structure of the CNDs, allowing for an effective electron transfer process, − which leads to efficient fluorescent quenching of the CNDs. The quenching of fluorescence intensity by different concentrations of Ho³⁺ was described using the Stern–Volmer equation, plotting the ratio of the fluorescence intensity of CNDs without Ho³⁺ and the fluorescence intensity observed for Ho³⁺-CNDs hybrids as a function of varying holmium­(III) concentrations (Figure ). One of the key characteristics of CNDs is their dual charge transfer behavior, enabling them to function as either electron donors or acceptors. This bifunctionality makes the charge transfer chemistry of CNDs highly versatile. The proposed REⁿ⁺-CNDs hybrid system is primarily based on the charge transfer process, where CNDs act as electron donors and holmium­(III) as the electron acceptor. To focus on the spectroscopic study of the hybrid system’s behavior, an aqueous medium was chosen to facilitate strong coupling between the holmium­(III) ions and water molecules, resulting in the quenching of the lanthanide fluorescence via energy transfer from the high-energy O–H vibrations of water molecules to the electronic states of holmium­(III). The above ensures that the only photoinduced fluorescence quenching process observed is that of the Ho³⁺-CNDs hybrid system. Under UV light excitation (365 nm), electrons in the CNDs transfer from the π to the π* energy level, passing through intermediate photoblinking states. Then, electrons in the LUMO level of the carbon atoms from the functional groups are transferred to the energy levels of Ho³⁺, resulting in a decrease in fluorescence intensity, i.e., fluorescence quenching.

9.

Fluorescence intensity plot (a–j), for different Ho³⁺-CNDs hybrids systems.

10.

Stern–Volmer plots of Ho³⁺-CNDs hybrids fluorescence intensity quenching by holmium­(III); [Ho³⁺] = 0.0 to 9 × 10^–5 M.

For the Stern–Volmer graph, a value of R ² = 0.9801 was obtained, with an equation that describes the turn-off behavior, I ₀/I = 1.16 × 10⁴ [Ho³⁺] + 1.0125, which allows us to know the value of the Stern–Volmer constant, K _sv = (1.16 × 10⁴ ± 5.52 × 10²) M^–1. Based on the standard deviation of the blank and the slope of the linear fit, the limit of detection (LOD) and limit of quantification (LOQ) were calculated as 1.60 and 5.35 μM, respectively. These values demonstrate the high sensitivity of the CNDs sensor for Ho³⁺ ions. The LOD was calculated based on three times the standard deviation rule, with ten blank measurements and LOQ to the rule of ten times the standard deviation. The detection of oxalate was based on a reactivation effect of the fluorescence intensity of the CNDs (turn-on) since the addition of the oxalate anions established a complexation equilibrium between oxalate anions (C₂O₄)^2– and Ho³⁺, allowing the formation of the complex [Ho­(C₂O₄)₃]^3– and stopping the electronic transfer process, i.e., quenching. The emission spectra of the Ho³⁺-CNDs hybrids with [Ho³⁺] = 9 × 10^–5 M mixed with oxalate (f–l) are shown in Figure . The PL spectrogram showed a change when the concentration of oxalate increased from 4.5 × 10^–5 to 3.6 × 10^–4 M, and the PL increased linearly.

11.

PL spectrograms of Ho³⁺-CNDs hybrids systems (f-l), with [Ho³⁺] = 9 × 10^–5 M, and different concentrations to oxalate [C₂O₄]^2–= 0.0 to 3.6 × 10^–4 M.

The molar extinction coefficient (ε) and quantum yield (ΦF) of the CNDs were not determined due to the absence of an exact molecular or molar concentration, which is a common limitation in the study of carbon-based nanomaterials. Since CNDs are heterogeneous systems composed of a mixture of nanostructures with undefined molecular weight, standard spectroscopic quantification methods based on molarity are not directly applicable. Additionally, the lack of certified quantum yield standards under comparable excitation conditions further limits accurate determination. Nevertheless, the photoluminescence behavior was characterized through relative intensity changes, suitable for evaluating sensor performance in this context.

To contextualize the performance of the developed CNDs sensor for Ho³⁺ detection, Table summarizes key parameters of similar CD-based sensors published in the literature, including linear ranges, detection limits, and sensing mechanisms. Many of these sensors operate over broader concentration intervals, ranging from low micromolar to tens of micromolar levels. In contrast, in this work, we chose to focus on a narrower linear range (0.00–90 μM). This decision was made to enhance the sensitivity of the fluorescence response and maximize the slope of the Stern–Volmer curve, which in turn contributes to achieving lower LOD and LOQ values. Besides offering competitive performance, our sensor uniquely allows for the sequential detection of Ho³⁺ ions and oxalate, a feature that has been little explored in previous CND-based studies. This dual capability, combined with improved trace-level sensitivity, makes our approach distinctive within the field of lanthanide sensing.

3. Comparison of the Linearity, LOD, and LOQ of CDs-Based Fluorescent Sensors.

sensor/analysis	target analyte	linear range (μM)	LOD (μM)	LOQ (μM)	references
Ho3+-CNDs	Ho3+/ (C2O4)2–	0–90	1.60	5.35
Am-CDs	S2O8 2–	1.96–15.59	0.94
CQDs for H. pylori genes	DNA	1.30–11.49	0.098
CQDs for Al3+	Al3+	0.15–38.46	0.1138
CDLP-D for Hg2+	Hg2+	1–40	2.5	8.3
CDs for Fe3+	Fe3+	30–600	9.55
CQDs for Cr6+	Cr6+	1–70	0.59

3.3. Photoinduced Charge-Transfer Interactions in a Ho³⁺-CNDs Hybrid: An Approximation from DFT

A DFT study was conducted to elucidate the interaction between Ho³⁺, [Ho­(C₂O₄)₃]^3–, and CNDs. Figure illustrates the C₆₀ fullerene with a carboxylate functional group in its ground state, isolated as well as interacting with Ho³⁺. The calculated distance between Ho³⁺ and oxygen was 2.248 Å, which closely aligns with previously reported values for similar systems. , Additionally, the interaction with Ho³⁺ resulted in a noticeable decrease in the angle between adjacent oxygen atoms, indicating that the oxygen atoms moved closer to each other as a result of the interaction. The behavior for the other two functional groups, the primary alcohol and the anhydride group, was similar. For the alcohol, the distance between the oxygen atom and Ho³⁺ was 2.281 Å (Supporting Information, Figure S1), while for the anhydride group, the distances between the holmium ion and the oxygen atoms were found to range from 2.283 to 2.319 Å (Supporting Information, Figure S6).

12.

Optimized structure obtained for (a) C₆₀ fullerene with the COO^– functional group and (b) C₆₀ fullerene with the COO^– functional group and Ho³⁺ in their ground states. Relevant bond lengths and angles are annotated.

To determine the type of chemical bond between the oxygen atom of the carboxylate functional group and Ho³⁺, a topological analysis was performed using Bader’s QTAIM. Figure illustrates the results of this analysis. Based on the values obtained at BCP for electron density ρ­(r) and Laplacian ∇²ρ­(r), it can be concluded that the bond between Ho³⁺ and oxygen is predominantly ionic. This assumption is supported by the criteria because ∇²ρ­(r) > 0 au, and ρ­(r) ranges from 0.0703 and 0.0712 au, which are consistent with the characteristics of ionic bonding interaction. For the alcohol and anhydride groups, similar results were obtained: in both cases, ionic bonding interactions were found, as shown in Figures S2 and S7 (Supporting Information), respectively.

13.

Molecular graphs of fullerene C₆₀ with COO^– and Ho³⁺ system with his electron density and Laplacian value in a.u. The small orange, yellow, and green dots represent the bond critical, ring critical, and cage critical points, respectively.

Figure presents the HOMO and LUMO plotted on isosurfaces with a density of 0.002 au for the C₆₀ fullerene functionalized with the COO^– group. The calculated energy gap, between HOMOα and LUMOα, is obtained as 1.371 eV. In contrast, the energy gap between HOMOβ and LUMOβ is 1.432 eV. Additionally, the gap between HOMOα and LUMOβ is 1.345 eV. Thus, E _g was assumed to be the latter one. The LUMO is predominantly localized near the COO^– group, highlighting its role as a preferred site for electron acceptance. In contrast, the HOMO is largely delocalized over the C₆₀ structure, suggesting potential regions for charge transfer across the molecule.

14.

Frontier orbitals HOMO and LUMO, alpha and beta, obtained for the C₆₀-COO^– complex at the B3LYP/6–31G level of theory. Energy gaps are annotated in eV.

Figure shows the HOMO and LUMO frontier orbitals for the C₆₀–COO^– complex after interaction with Ho³⁺, as compared to those shown in Figure for the system without the holmium ion. Energy levels of the HOMO and LUMO obtained for the system with Ho³⁺ differ significantly from those of the C₆₀-COO^– complex without holmium­(III), as detailed in Table . Notably, the energy gap between HOMOα and LUMOβ is smaller for the complex with Ho³⁺ (1.264 eV) than for the complex without it (1.345 eV). Similarly, the energy gap between HOMOα and LUMOα calculated in the case of the C₆₀-COO^–-Ho³⁺ system (1.343 eV) is lower than the corresponding value in the absence of Ho³⁺ (1.371 eV). Additionally, the gap for the beta orbitals (1.385 eV) is slightly reduced compared to the unmodified system (1.432 eV). The inclusion of Ho³⁺ induces significant changes in the electronic structure of the C₆₀–COO^– system. Unlike the unmodified complex, where the LUMO was predominantly localized near the COO^– group, the LUMO in this case is distributed away from both the COO^– group and Ho³⁺, suggesting a redistribution of electron density influenced by the holmium ion. In contrast, the HOMO remains largely delocalized over the entire system.

15.

Frontier orbitals HOMO and LUMO, alpha and beta, obtained for the C₆₀-COO^– -Ho³⁺ system at the B3LYP/6–31G, def2-TZVP level of theory.

4. Energetic Parameters Obtained for C₆₀-Modified Complexes with and without the Ho³⁺ .

system	E HOMOα (eV)	E HOMOβ (eV)	E LUMOα (eV)	E LUMOβ (eV)
C60-COO–	–2.166	–2.253	–0.795	–0.821
C60-COO–-Ho3+	–10.967	–11.088	–9.624	–9.703
C60-CO	–5.317	–6.048	–3.244	–3.809
C60-CO-Ho3+	–13.396	–13.444	–13.014	–12.781
C60-anh	–5.490		–3.918
C60-anh -Ho3+	–13.033	–13.414	–12.233	–12.085

Figure shows the charge distribution and electrostatic potential (ESP) map for the C₆₀–COO^– system, both (a) isolated and (b) interacting with Ho³⁺. The Mulliken charge distributions were calculated from their ground state configurations, and the ESP was mapped onto isosurfaces with an electron density of 0.0004 au. Before the interaction with Ho³⁺, the highest ESP region, arising from positive Mulliken charges, was located around the carbon atom of the COO^– functional group with a positive charge of 0.474 e. Conversely, the regions with the lowest ESP were found around the oxygen atoms of the carboxylate group, with charges ranging from −0.405 to −0.367 e. Overall, C₆₀ fullerene exhibits a net negative charge before the interaction, as corroborated in Table . Upon interaction, the fullerene C₆₀ develops a positive ESP region surrounding itself, while the charge of Ho³⁺ decreases from +3 to +1.313, indicating significant charge transfer from the C₆₀ fullerene to the holmium ion. The lowest ESP region remains localized on the oxygen atoms of the carboxylate group, but their charges shift to a range of −0.547 to −0.546 e, suggesting that after the interaction, electron density flows from the C₆₀ fullerene to the functional group, further modifying the electronic structure of the complex.

16.

Mulliken charge distribution and ESP, mapped on isosurfaces with 0.0004 au of electron density, of the complex C₆₀-COO^– (a) isolated (b) with Ho³⁺. Charges and ESP values are annotated in atomic units.

5. MPA and HPA for C₆₀-COO^– Complex Interacting with Ho³⁺ .

compound	Mulliken charge before Ho3+ interaction	Hirshfeld charge before Ho3+ interaction	Mulliken charge after holmium ion interaction	Hirshfeld charge after holmium ion interaction
COO–	–0.298	–0.234	–0.573	–0.432
C60	–0.702	–0.766	+1.259	+1.244
Ho3+	+3	+3	+1.313	+1.188

The Mulliken Population Analysis (MPA) provided an initial understanding of the charge transfer process. However, Hirshfeld Population Analysis (HPA) was performed to achieve a more robust and accurate evaluation. This approach was chosen because Hirshfeld charges are less dependent on the basis set used for optimization, enabling a more reliable assessment of the charge transfer process. Table shows the results obtained from both MPA and HPA. In both cases, it is evident that charge transfer occurs from the C₆₀ fullerene to the functional group and Ho³⁺, which is consistent with the ESP results shown in Figure .

For the alcohol and anhydride functional groups, although a similar trend was observed in the charge transfer process, a notable difference arises when compared to the COO^– group. In that case, electrons were transferred exclusively from the C₆₀ fullerene to the Ho³⁺ ion and functional group. However, for the alcohol and anhydride systems, electrons were transferred from both the fullerene and functional groups to Ho³⁺. This distinction is evident from the observed increase in the charges of both components after their interaction with the holmium ion, as detailed in Tables S1 and S2, Supporting Information). Additionally, their frontier molecular orbitals and ESP maps were also obtained to corroborate the charge transfer process, as shown in the Supporting Information.

Considering the charged nature of the systems studied, a basis set including diffuse and polarization functions, 6–31++G­(d,p) was employed to compare its performance against the smaller 6–31 G set. This comparison was applied to one of the representative systems, C₆₀-anh-Ho³⁺. As shown in the Supporting Information, the results obtained with 6–31++G­(d,p) were found to be consistent with those obtained using 6–31 G. The bond lengths between oxygen and Ho³⁺ for the new method (Figure S11) differ by only 0.001 Å. Similarly, the molecular graph reveals that both the electron density and its Laplacian vary only slightly, with differences well below 0.01 au, supporting the conclusion that the Ho–O interaction remains ionic with the new basis set (Figure S12). The HOMO–LUMO frontier orbitals exhibit similar spatial distributions and energy gaps with a maximum deviation of 0.089 eV using the extended basis set (Figure S13). Moreover, the ESP maps show comparable distributions with slightly more positive regions near the fullerene core when using 6–31++G­(d,p), although the difference is not significant (Figure S14). Additionally, the Mulliken charge on Ho³⁺ changes by only 0.049e. Considering the minimal variations observed and the increased computational cost associated with diffuse and polarization functions, the 6–31G basis set was employed for all other systems to optimize computational resources.

To provide a deeper understanding of the electronic, energetic, and chemical reactivity properties of the Ho³⁺–CNDs systems, various global and local descriptors were calculated and are summarized in Table . These descriptors are based on Pearson’s HSAB theory. The calculated parameters include vertical ionization energy (I), vertical electron affinity (A), global hardness (η = (I – A)/2), chemical potential (μ = −(I + A)/2), and electrophilicity (ω = μ²/2η). To further explore the charge transfer processes between Ho³⁺ and the CNDs, the Electrophilicity-Based Charge Transfer (ECT, eq )) descriptor was calculated. In addition, the fraction of electrons transferred (ΔN, eq ) was evaluated. Both metrics were computed using the optimized geometries and provide a quantitative estimation of the direction and magnitude of electron transfer based on the global reactivity parameters.

$$\mathrm{ECT}=2[({{\omega }_{\mathrm{Ho}}}^{3+}/{{\chi }_{\mathrm{Ho}}}^{3+})-({\omega }_{\mathrm{CNDs}}/{\chi }_{\mathrm{CNDs}})]$$ 5

$$\mathrm{\Delta }N=({\mu }_{\mathrm{CNDs}}-{{\mu }_{\mathrm{Ho}}}^{3+})/[2({{\eta }_{\mathrm{Ho}}}^{3+}+{\eta }_{\mathrm{CNDs}})]$$ 6

6. Energetic and Global Parameters Obtained for Their Ground State Structure and the Interacting System of Interest.

system	I eV	A eV	η eV	χ eV	μ eV	ω eV	ΔN	ECT
[Ho3+]	43.600	22.631	10.485	33.116	–33.116	52.298
C60-COO–	3.750	–0.732	2.241	1.509	–1.509	0.508	1.242	2.485
C60-CO	6.486	2.650	1.918	4.568	–4.568	5.439	1.151	0.777
C60-anh	6.651	2.751	1.950	4.701	–4.701	5.667	1.143	0.748

Table presents the electronic parameters obtained from the calculations. It can be observed that both the ECT descriptor and the ΔN have positive values, indicating that the charge transfer process occurs from the CNDs to the Ho³⁺ ion in all three cases. This finding is consistent with the Mulliken and Hirshfeld charge analyses. Additionally, the ΔN values are similar across the three systems, suggesting that the extent of charge transfer remains comparable. This trend is also reflected in the Mulliken and Hirshfeld results, which show charge redistribution of similar magnitude in all cases.

To analyze theoretically the electronic transitions and the orbital contributions involved, natural transition orbitals (NTOs) were calculated using time-dependent DFT (TDDFT). For this purpose, the same basis set (6–31G) was used; however, the functional was adjusted to CAM-B3LYP, as this corrected functional provides improved accuracy for describing charge-transfer excitations and long-range interactions. The theoretical UV–vis spectra obtained for the three CND systems show a good agreement with the experimental results (Figure ). The best match was observed for the C₆₀-anh complex, which exhibits absorption bands at 244.76 and 285.63 nm (Figure ), consistent with those reported experimentally. In the case of the C₆₀-COO^– system, an absorption band appears around 301.31 nm (Figure S15), which is close to the experimental band at 280 nm. The C₆₀-CO systems display a band at 285.25 nm (Figure S16), aligned with a peak in the experimental data. Additionally, the NTOs corresponding to the main excitations of each system are included, providing insight into the electronic nature of the transitions for C₆₀-anh (Figure ), C₆₀–COO^– (Figure S15), and C₆₀–CO (Figure S16) complexes. Overall, the similarity of the UV–Vis spectra across the three systems supports the idea that the fullerene C₆₀ core can serve as a reasonable first approximation for modeling CND-based systems. The observed discrepancies may be attributed to the fact that the experimental CNDs are surrounded by multiple functional groups, whereas in this theoretical study, only a single functional group was considered an approximation.

17.

Calculated UV–vis absorption spectrum of the C₆₀-anh complex and representative NTOs for the excitations at 244.76 and 285.63 nm, obtained by TDDFT at the CAM-B3LYP/6–31G level of theory.

On the other hand, Figure illustrates the [Ho­(C₂O₄)₃]^3– complex in its ground state. The calculated distances between Ho³⁺ and oxygen atoms range from 2.287 to 2.290 Å, which agrees with previously reported values for similar systems. ,

18.

Optimized structure obtained for the [Ho­(C₂O₄)₃]^3– complex in the ground state calculated at the B3LYP/6–31G, def2-TZVP level of theory. Relevant bond lengths and angles are annotated.

To investigate the chemical bonding between oxygen atoms of (C₂O₄) ^2– and Ho³⁺ in [Ho­(C₂O₄)₃]^3–, a topological analysis was performed using Bader’s QTAIM. Figure illustrates the results focusing on the six BCP associated with Ho³⁺-oxygen interactions. The values of ρ­(r) ranging from 0.0610 to 0.0617 au, and its Laplacian ∇²(ρ­(r)) > 0 at these points reveal an ionic bonding interaction, which agrees with the results obtained for the C₆₀-COO^– complex.

19.

Molecular graph of [Ho­(C₂O₄)₃]^3– system with his electron density and Laplacian value in au. The small orange, yellow, and green dots represent the bond, ring, and cage critical points, respectively.

Figure presents the HOMO and LUMO plotted on isosurfaces with a density of 0.002 au for the [Ho­(C₂O₄)₃]^3– complex. The energy of the LUMO orbital is 8.314 eV, while that for HOMO is 2.954 eV, which gives an energy gap of 5.360 eV. The HOMO is primarily localized on the oxalate ligands, with minor contributions near Ho³⁺, while the LUMO is also distributed over the oxalate ligands, indicating the dominance of the ligands in these frontier orbitals. The calculated bandgap of 5.360 eV is significantly larger than that of C₆₀-COO-Ho³⁺ system, suggesting enhanced electronic stability and reduced charge transfer reactivity.

20.

Frontier orbitals HOMO and LUMO obtained for the [Ho­(C₂O₄)₃]^3– complex at the B3LYP/6–31G, def2-TZVP level of theory.

Figure shows the charge distribution and ESP map for the [Ho­(C₂O₄)₃]^3– complex. The Mulliken charge distributions were calculated from their ground state configurations, and the ESP was mapped onto isosurfaces with an electron density of 0.0004 au. The highest ESP region, arising from positive Mulliken charges, is located around the carbon atom of the oxalate (C₂O₄)^2–, with a positive charge of about 0.447–0.448 e. Conversely, the regions with the lowest ESP are around the oxygen atoms surrounding the holmium­(III) ion, with charges ranging from −0.598 to −0.596 e. The interaction between the oxalate ligand (C₂O₄)^2– and Ho³⁺ results in a decrease in the charge of Ho³⁺ from +3 to +1.132, indicating significant charge transfer from the oxalate anions to the holmium ion.

21.

Mulliken charge distribution and ESP, mapped on isosurfaces with 0.0004 au of electron density, of the complex [Ho­(C₂O₄)₃]^3–.

In both the C₆₀–COO^––Ho³⁺ system and the [Ho­(C₂O₄)₃]^3– complex, a charge transfer process from the organic molecule to Ho³⁺ is observed, as evidenced by the reduction in the holmium’s calculated charge in both cases. Additionally, QTAIM analysis reveals that both systems exhibit chemical bonding characteristics consistent with ionic interactions. Furthermore, the [Ho­(C₂O₄)₃]^3– complex appears to be more stable, as indicated by its larger energy gap compared to the C₆₀-COO^–-Ho³⁺ system.

4. Conclusions

The results obtained in this study revealed that the interaction between Ho³⁺ and CNDs leads to the formation of a hybrid (REⁿ⁺-CNDs), which can be experimentally observed through fluorescence quenching of the CNDs. This behavior is theoretically supported by Bader’s QTAIM analysis, considering Laplacian and charge density values. Additionally, the study by Mulliken and Hirshfeld reveals a charge transfer process from CNDs to the lanthanide ion, which is crucial for understanding the electronic interactions between these two components in the studied system.

Moreover, the fluorescence “turn-on” process, observed upon the addition of oxalate anions, was experimentally confirmed by the restoration of the fluorescence. This phenomenon was theoretically validated through QTAIM and electronic structure analysis, contributing to a better understanding of the mechanism involved in fluorescence recovery. These results establish a solid foundation for the development of an on–off sensor capable of simultaneously detecting holmium ions and oxalate anion.

Furthermore, computational optimization of the compounds was achieved using DFT with the B3LYP functional and the def2-TZVP and 6–31G basis sets, allowing for consistent results that correlate with experimental findings and theoretical predictions. The charge transfer process was quantitatively characterized by means of Mulliken and Hirshfeld population analyses. In addition, the changes in the electronic structure of the complexes were studied by means of frontier molecular orbitals. These findings not only provide valuable insights into the interaction between CNDs and lanthanide ions but also open up new possibilities for designing advanced sensors with practical applications in the detection of relevant compounds.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c04086.

• Optimized geometries of the C₆₀–CO–Ho³⁺ (Figure S1) and C₆₀–anh–Ho³⁺ (Figure S6) systems. For both complexes, the corresponding molecular graphs (Figures S2 and S7), frontier molecular orbitals (Figures S3, S4, S8, and S9), and ESP maps (Figures S5 and S10) are also provided. Mulliken and Hirshfeld charge analyses for these complexes are summarized in Tables S1 and S2. Furthermore, an extended basis set analysis is included for the C₆₀–anh–Ho³⁺ system (Figures S11–S14), along with TDDFT results for the C₆₀-COO^– (Figure S15) and C₆₀-CO (Figure S16) complexes. Finally, Cartesian coordinates for all optimized geometries (Tables S3–S10) and details of the TDDFT calculations performed are listed (PDF)

The APC was funded by Tecnológico de Monterrey through grants for scientific papers publication fund.

The authors declare no competing financial interest.